Keeper Chris Keenan departs from Crusaders
Dungannon have confirmed that O'Neill has left the Swifts and he appears set for a move to the Premiership runners-up and beaten Irish Cup finalists.
Prior to the Cup final, there were reports that Keenan was likely to exit from the Crues.
Keenan was then at fault for Linfield's winner in the Cup decider.
Dungannon have said that Niall Morgan will be their goalkeeper in the coming season after agreeing a new two-year deal with the Swifts.